{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "nbsphinx": "hidden"
   },
   "source": [
    "# Random Signals and LTI-Systems\n",
    "\n",
    "*This jupyter notebook is part of a [collection of notebooks](../index.ipynb) on various topics of Digital Signal Processing. Please direct questions and suggestions to [Sascha.Spors@uni-rostock.de](mailto:Sascha.Spors@uni-rostock.de).*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction\n",
    "\n",
    "The response of a system $y[k] = \\mathcal{H} \\{ x[k] \\}$ to a random input signal $x[k]$ is the foundation of statistical signal processing. In the following we limit ourselves to [linear-time invariant (LTI) systems](https://en.wikipedia.org/wiki/LTI_system_theory).\n",
    "\n",
    "![LTI system](LTI_system_td.png)\n",
    "\n",
    "In the following it is assumed that the statistical properties of the input signal $x[k]$ are known. For instance, its first- and second-order ensemble averages. It is further assumed that the impulse response $h[k]$ or the transfer function $H(e^{\\,\\mathrm{j}\\,\\Omega})$ of the LTI system is given. We are looking for the statistical properties of the output signal $y[k]$ and the joint properties between the input $x[k]$ and output $y[k]$ signal."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Stationarity and Ergodicity\n",
    "\n",
    "The question arises if the output signal $y[k]$ of an LTI system is (wide-sense) stationary or (wide-sense) ergodic for an input signal $x[k]$ exhibiting the same properties.\n",
    "\n",
    "Let's assume that the input signal $x[k]$ is drawn from a stationary random process. According to the [definition of stationarity](../random_signals/stationary_ergodic.ipynb#Definition) the following relation must hold\n",
    "\n",
    "\\begin{equation}\n",
    "E\\{ f(x[k_1], x[k_2], \\dots) \\} = E\\{ f(x[k_1 + \\Delta], x[k_2 + \\Delta], \\dots) \\}\n",
    "\\end{equation}\n",
    "\n",
    "where $\\Delta \\in \\mathbb{Z}$ denotes an arbitrary (temporal) shift and $f(\\cdot)$ an arbitary mapping function. The condition for time-invariance of a system reads\n",
    "\n",
    "\\begin{equation}\n",
    "y[k + \\Delta] = \\mathcal{H} \\{ x[k + \\Delta] \\}\n",
    "\\end{equation}\n",
    "\n",
    "for $y[k] = \\mathcal{H} \\{ x[k] \\}$. Applying the system operator $\\mathcal{H}\\{\\cdot\\}$ to the left- and right-hand side of the definition of stationarity for the input signal $x[k]$ and recalling the linearity of the expectation operator $E\\{\\cdot\\}$ yields\n",
    "\n",
    "\\begin{equation}\n",
    "E\\{ g(y[k_1], y[k_2], \\dots) \\} = E\\{ g(y[k_1 + \\Delta], y[k_2 + \\Delta], \\dots) \\}\n",
    "\\end{equation}\n",
    "\n",
    "where $g(\\cdot)$ denotes an arbitrary mapping function that may differ from $f(\\cdot)$. From the equation above, it can be concluded that the output signal of an LTI system for a stationary input signal is also stationary. The same reasoning can also be applied to an [ergodic](../random_signals/stationary_ergodic.ipynb#Ergodic-Random-Processes) input signal. Since both wide-sense stationarity (WSS) and wide-sense ergodicity are special cases of the general case, the derived results hold also here.\n",
    "\n",
    "Summarizing, for an input signal $x[k]$ that is\n",
    "\n",
    "* (wide-sense) stationary, the output signal $y[k]$ is (wide-sense) stationary and the in- and output is jointly (wide-sense) stationary\n",
    "* (wide-sense) ergodic, the output signal $y[k]$ is (wide-sense) ergodic and the in- and output is jointly (wide-sense) ergodic\n",
    "\n",
    "This implies for instance, that for a WSS input signal $x[k]$ measures like the auto-correlation function (ACF) can also be applied to the output signal $y[k] = \\mathcal{H} \\{ x[k] \\}$ of an LTI system."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example - Response of an LTI system to a random signal\n",
    "\n",
    "The following example computes and plots estimates of the linear mean $\\mu[k]$ and auto-correlation function (ACF) $\\varphi[k_1, k_2]$ for the in- and output of an LTI system. The input $x[k]$ is drawn from a normally distributed white noise process."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1000x500 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1000x500 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "L = 64  # number of random samples\n",
    "N = 1000  # number of sample functions\n",
    "\n",
    "# generate input signal (white Gaussian noise)\n",
    "np.random.seed(1)\n",
    "x = np.random.normal(size=(N, L))\n",
    "# generate output signal\n",
    "h = 2 * np.fft.irfft([1, 1, 1, 0, 0, 0])\n",
    "y = np.asarray([np.convolve(x[n, :], h, mode=\"same\") for n in range(N)])\n",
    "\n",
    "\n",
    "def compute_plot_results(x):\n",
    "    \"\"\"Compute and plot linear mean and ACF\"\"\"\n",
    "\n",
    "    # estimate linear mean by ensemble average\n",
    "    mu = 1 / N * np.sum(x, 0)\n",
    "    # estimate the auto-correlation function\n",
    "    acf = np.zeros((L, L))\n",
    "    for n in range(L):\n",
    "        for m in range(L):\n",
    "            acf[n, m] = 1 / N * np.sum(x[:, n] * x[:, m], 0)\n",
    "\n",
    "    plt.subplot(121)\n",
    "    plt.stem(mu)\n",
    "    plt.title(r\"Estimate of linear mean $\\hat{\\mu}[k]$\")\n",
    "    plt.xlabel(r\"$k$\")\n",
    "    plt.ylabel(r\"$\\hat{\\mu}[k]$\")\n",
    "    plt.axis([0, L, -1.5, 1.5])\n",
    "\n",
    "    plt.subplot(122)\n",
    "    plt.pcolor(np.arange(L + 1), np.arange(L + 1), acf, vmin=-2, vmax=2)\n",
    "    plt.title(r\"Estimate of ACF $\\hat{\\varphi}[k_1, k_2]$\")\n",
    "    plt.xlabel(r\"$k_1$\")\n",
    "    plt.ylabel(r\"$k_2$\")\n",
    "    plt.colorbar()\n",
    "    plt.autoscale(tight=True)\n",
    "\n",
    "\n",
    "plt.figure(figsize=(10, 5))\n",
    "plt.gcf().suptitle(r\"Input signal $x[k]$\", fontsize=12)\n",
    "compute_plot_results(x)\n",
    "\n",
    "plt.figure(figsize=(10, 5))\n",
    "plt.gcf().suptitle(r\"Output signal $y[k]$\", fontsize=12)\n",
    "compute_plot_results(y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise**\n",
    "\n",
    "* Are the in- and output signals WSS?\n",
    "* Can the output signal $y[k]$ be assumed to be white noise?\n",
    "\n",
    "Solution: From the shown results it can assumed for the input signal $x[k]$ that the linear mean $\\mu_x[k]$ does not depend on the time-index $k$ and that the ACF $\\varphi_{xx}[k_1, k_2]$ does only depend on the difference $\\kappa = k_1 - k_2$ of both time indexes. The same holds also for the output signal $y[k]$. Hence both the in- and output signal are WSS. Although the input signal $x[k]$ can be assumed to be white noise, the output signal $y[k]$ is not white noise due to its ACF $\\varphi_{yy}[k_1, k_2]$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbsphinx": "hidden"
   },
   "source": [
    "**Copyright**\n",
    "\n",
    "This notebook is provided as [Open Educational Resource](https://en.wikipedia.org/wiki/Open_educational_resources). Feel free to use the notebook for your own purposes. The text is licensed under [Creative Commons Attribution 4.0](https://creativecommons.org/licenses/by/4.0/), the code of the IPython examples under the [MIT license](https://opensource.org/licenses/MIT). Please attribute the work as follows: *Sascha Spors, Digital Signal Processing - Lecture notes featuring computational examples*."
   ]
  }
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